Grammar of Time GT-03: Hilbert and Born as Re-Closure of Coherent Portato

Hilbert is before the trace. Born is after the question. GT-03 is a technical sector module of the Grammar of Time programme. It does not claim to derive all of quantum mechanics, quantum dynamics, quantum field theory, or the full Hilbert-space formalism from nothing. Its narrower claim is that, given a stabilized measurement regime with finite closure channels, square-root access to response weights, reversible phase memory, and recomposable channels, the Hilbert representation is the minimal coherent-portato completion. Given this Hilbert representation, any operationally coherent record-weight on effects is forced to have the trace form R_omega(E) = Tr(rho_omega E). Thus GT-03 eliminates two primitives in the measurement regime: primitive Hilbert space as an unexplained arena, and primitive quantum probability as an unexplained postulate. The trace representation is treated as a finite-dimensional effect-valuation result; the GT contribution is the primitive audit of the closure, coarse-graining, quotient, stability, mixing, and covariance locks. Born is not primitive probability: it is the record-weight of coherent portato forced to re-close through a question. This is a technical preprint, version v1.0, and has not been peer-reviewed.